Temporal growth of the h-index in a diachronous cumulative time series is predicted to be linear by Hirsch (2005), whereas other models predict a concave increase. Actual data generally yield a linear growth or S-shaped growth. We study the h-index's growth in computer simulations of the publication-citation process. In most simulations the h-index grows linearly in time. Only occasionally does an S-shape occur, while in our simulations a concave increase is very rare. The latter is often signalled by the occurrence of plateaus - periods of h-index stagnation. Several parameters and their influence on the h-index's growth are determined and discussed.